Sentence examples for underlying equation of the from inspiring English sources

The underlying equation of the MCTDH method is [ Eq. (1)]: (1) where Q1,.., Q f are the nuclear coordinates, the expansion coefficients and the SPFs for each degree of freedom κ.

This part-1 introduces the structure, principles and the underlying equations of the modular simulation system.

Our formulation is independent of the underlying equation of state.

Masemola et al. in [22] have recently applied the Lie symmetry method to construct the conservation laws and the exact solutions of the underlying equation for the special cases (m=2) and (alpha=-1).

As a result, and in contrast to the approach by Guermond et al. (2011), we do not modify the underlying equations of relativistic hydrodynamics by introducing additional entropy-related terms.

The protagonist, a university professor, "is forced to abandon scepticism and discover the underlying equations of magic, via symbolic logic", in critic David Langford's description.

Nonlinearity and control input exist both in the drift and diffusion terms of the underlying equation, and the control problem of interest is considered in the framework with a novel Banach space.

One may notice from the next theorem that in this case the parameter θ exists in the conditions, therefore the boundedness of the underlying equation may not be fully reproduced under the same conditions.

This type of modeling uses a physical network approach to model building: only requires to join the physical components with physical connections to define the underlying dynamic equations of the system to be modeled.

Optimization-oriented reduced-order models should target a particular output functional, span an applicable range of dynamic and parametric inputs, and respect the underlying governing equations of the system.

However, given that oscillations are often structurally not robust (structural robustness refers to whether the behavior of a system is robust to minor modifications of the form of the underlying equations), it is surprising that the question of robustness has been largely ignored in the context of the RQH.